A few documents I wrote Here are a few documents that are official somehow and linked to a public event. 2nd year of PhD (2022-2023) My PhD thesis is on higher-order automata and related topics. Here is: My talk “Profinite $\lambda$-terms and parametricity” links profinite $\lambda$-terms to regular languages of $\lambda$-terms à la Salvati through Stone duality. I did it: the 20th of April at SYCO 11 (video), the 25th of April at the WG6 meeting, the 26th of May at the PPS days 2023, the 1st of June at the Séminaire Logique et Interaction. I did a talk entitled A quick introduction to higher-order automata on the 21th of October 2022 at the ASV day 2022. My talk “From profinite words to profinite $\lambda$-terms” is about the link between profinite words and Reynolds parametricity. I did it: the 19th of September 2022 at CaCS 2022 (slides, video), the 22nd of September 2022 at the Resources in Computation project meeting (slides), the 12nd of October 2022 at the LHC days 2022 (slides), the 2nd of December 2022 at the RECIPROG mini-workshop (slides), the 6th of January 2023 at the 4th ANR PPS general meeting (slides). The Categories for the uninitiated talk I gave the 15th of September 2022 at the non-permanent seminar at IRIF. 1st year of PhD (2021-2022) Here are a few talks that I gave during my first year of PhD: The From profinite words to profinite $\lambda$-terms talk I gave the 4th of July 2022 at the Structure Meets Power workshop, Paris (abstract) The Profinite $\lambda$-terms and more talk I gave the 19th of May 2022 at the Duality and more workshop, Nice The Topology and Categories for higher-order automata talk I gave the 12th of April 2022 at MGS 2022, Nottingham Master internship (2021) I wrote things about canonical extensions, which were the topic of my M2 research internship from March 2021 to August 2021 under the supervision of Sam van Gool and Paul-André Melliès. You can find here the following documents: A presentation of linear logic-related applications of canonical extensions which I used during the ASV day on the 19th November. A truncated version of my internship defense slides that I used during the PPS day, the 13th October. The presentation used for the internship defense on the 3rd of September. The report, respecting the 20 pages limit and sent on the 20th of August.